Dunkl Translation and Uncentered Maximal Operator on the Real Line
We establish estimates of the Dunkl translation of the characteristic function χ[−ɛ,ɛ], ɛ>0, and we prove that the uncentered maximal operator associated with the Dunkl operator is of weak type (1,1). As a consequence, we obtain the Lp-boundedness of this operator for 1<p≤+∞.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/87808 |
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| Summary: | We establish estimates of the Dunkl translation of
the characteristic function χ[−ɛ,ɛ],
ɛ>0, and we prove that the uncentered maximal operator
associated with the Dunkl operator is of weak type (1,1). As a consequence, we obtain the Lp-boundedness of this operator for
1<p≤+∞. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |